Math 275/Stat 375 – Mathematical problems in Machine Learning

This class provides an introduction to a certain number of theoretical ideas that have been developed with the objective of understanding modern deep learning methods. Specific topics might include

Empirical risk minimization and empirical process theory:

• Uniform convergence guarantees

• Complexity bounds for neural networks

Optimization and implicit regularization:

• Linear models

• Nonlinear models

Generalization in the linear regime:

• The interpolation phase transition

• Random features models

• Neural tangent models

Feature learning:

• Mean field theory

• Other parametrizations

• Sparse and multi-index models

Diffusion models

• Guarantees

• Connections with stochastic localization

Attentions and transformers:

• Examples of in-context learning

Learning out of distribution

Class Times and Location

• Tue-Thu, 9:00-10:20AM

• Sequoia 200

Office hours

• Thu, 2:30-3:30PM (Starting on 4/18)

• Sequoia 133